DETECTING  EFFICIENCY   OF   THE   RESISTANCE- 

CAPACITY  COUPLED  AMPLIFIER 

TO  6000  METERS 


DISSERTATION 

SUBMITTED  TO  THE  BOARD  OF  UNIVERSITY  STUDIES 
OF  THE  JOHNS  HOPKINS  UNIVERSITY. 

IN  CONFORMITY  WITH  THE  REQUIREMENTS  FOR  THE 
DEGREE  OF  DOCTOR  OF  PHILOSOPHY. 


BY 
W.  G.  BROMBACHER 


BALTIMORE 
1922 


DETECTING  EFFICIENCY   OF   THE   RESISTANCE- 

CAPACITY  COUPLED  AMPLIFIER 

TO  6000  METERS 


DISSERTATION 

SUBMITTED  TO  THE  BOARD  OF  UNIVERSITY  STUDIES 
OF  THE  JOHNS  HOPKINS  UNIVERSITY. 

IN  CONFORMITY  WITH  THE  REQUIREMENTS  FOR  THE 
DEGREE  OF  DOCTOR  OF  PHILOSOPHY. 


BY 
W.  G.  BROMBACHER 


BALTIMORE 
1922 


<"* 


[Reprinted  from  THE  PHYSICAL  REVIEW,  S.S.,  Vol.  XX.,  No.  5.  November, 


DETECTING  EFFICIENCY  OF  THE  RESISTANCE-CAPACITY 
COUPLED   AMPLIFIER  TO   6,000    METERS. 

BY  W.  G.  BROMBACHER. 

SYNOPSIS. 

Detecting  Efficiency  and  Current  Amplification  of  the  Resistance-capacity  Coupled, 
Two-tube  Amplifier. — Test  of  Hulburt's  formula,  giving  a  relation  between  detecting 
efficiency  and  the  constants  of  the  tubes  and  circuits,  has  been  extended  to  6,000 
meters.  The  detecting  efficiency  is  defined  as  bo/A2,  where  A  and  bo  are  the  ampli- 
tudes, respectively,  of  the  input  grid  potential  and  of  the  rectified  component  of 
the  output  plate  current.  It  was  found  that  (i)  for  any  wave-length  the  relation 
between  60  and  A2  is  linear;  (2)  for  constant  wave-length,  bo/A2  varied  with  the 
coupling  capacity  in  accordance  with  the  formula  within  about  10  per  cent.,  being 
practically  constant  for  capacities  greater  than  200  /z^  F;  (3)  for  constant  capacities, 
bojA2  varied  with  wave-length  for  ranges  1,100  to  2,500  and  2,500  to  6,000  meters  in 
fair  agreement  with  the  theoretical  curve.  The  current  amplification,  n  =  bo/Eg*, 
where  Eg  is  the  amplitude  of  the  potential  impressed  on  the  grid  of  the  second 
tube,  was  found  to  be  independent  of  the  wave-length  to  6,000  meters. 

Plate  current  of  vacuum  tube  (Radiatron  UV  201)  was  found  to  be  sensitive  to  the 
external  temperature. 

i .   INTRODUCTORY. 

The  detecting  efficiency  of  the, resistance-capacity  coupled  electron 
tube  amplifier  has  been  discussed  by  E.  O.  Hulburt.1  He  derived  a 
formula  which  indicated  the  connection  between  it  and  the  constants  of 
the  electron  tubes  and  the  coupling  circuits.  His  experiments  showed 
that  the  theoretical  relation  held  in  the  region  from  400  to  1,600  meters. 

The  detecting  efficiency  was  defined  by  the  relation  lim  — -a  ,  in  which 

A-+oAZ 

A  and  60  are  the  amplitudes,  respectively,  of  the  input  grid  potential 
and  of  the  rectified  component  of  the  output  plate  current. 

Consider  the  high  frequency  amplifier  of  two  tubes  as  shown  in  Fig.  i . 


1  PHYS.  REV.,  18,  165,  1921. 


Fig.  1. 


543906 


1  [SECOND 

434  W.    G.    BROMBACHER.  [SERIES. 

For  this  type  of  amplifier  Hulburt  derived  the  following  formula,  subject 
to  the  conditions  that  there  be  no  rectification  in  the  first  tube  and  no 
grid  filament  current  in  the  second  tube 

gs) 


in  which  ^4  is  the  amplitude  of  the  radio  frequency  potential  impressed 
on  the  grid  of  the  first  tube,  b0  is  the  rectified  component  of  the  resulting 
radio  frequency  current  in  the  plate  circuit  of  the  second  tube;  k  is  the 
amplification  constant  of  the  first  tube.  r\  is  the  internal  resistance  of 
the  first  tube  from  filament  to  plate.  C5  is  the  filament-grid  capacity  of 
the  second  tube.  Resistances  r%  and  r$  and  capacity  £4  are  as  shown 
in  Fig.  i. 

Let  co/27r  be  the  frequency  of  the  impressed  voltage. 
Let 

-  =  gi,         o>C4  =  Xt, 
ri 

-  =  gi,        wC5  =  X6. 
r<i 

i 

-   =   g3, 

r« 

One  term  has  not  been  defined,  which  is 

n"W 

where  EQ  is  the  amplitude  of  potential  impressed  on  the  grid  of  the 
second  tube,     n  does  not  depend  on  the  frequency  of  the  impressed 
voltage.     (See  Fig.  6.) 
Let 

gigs  —  x&f,  =  a, 

Xi(g2   +  gs)    +  Xbg2    =    b. 


Then,  more  accurately,  the  formula  may  be  written 

a(a  +  gig3)  +  b(b  +  x^  -+ 


It  is  to  be  noticed  that  this  formula  gives  the  detecting  efficiency  in  terms 


VoL.^XX.  j  DETECTING   EFFICIENCY   OF   AMPLIFIER.  435 

of  the  constants  of  the  electron  tubes  and  the  coupling  circuits.  Also 
Formula  (i)  is  an  approximation  of  (2),  the  use  of  which  is  justified  under 
obvious  conditions. 

The  object  of  this  paper  is  to  make  the  experimental  measurements 
necessary  in  order  to  test  Formula  (i)  for  long  wave-lengths,  and  to  this 
end  measurements  were  made  from  1,000  to  6,200  meters. 

2.   APPARATUS. 

The  apparatus  consisted  of  a  condenser  potential  divider,  the  amplifier 
and  a  D'Arsonval  galvanometer.  The  arrangement  is  essentially  that 
of  Fig.  i.  The  potential  divider  consisted  of  the  coil  L,  the  Weston 
thermo-galvanometer  T,  and  the  condensers  Ci,  C2  and  C3.  This  appa- 
ratus has  been  previously  described  by  Hulburt  and  Breit.1  The  poten- 
tial impressed  on  the  grid  of  first  tube  may  be  found  from 

A  ___  — 
" 


C2  +  CiC8  +  C2C3) 

in  which  I  is  the  effective  current  measured  by  T.  By  coupling  L  to  a 
suitable  electron  tube  generating  set,  unmodulated  high-frequency  voltage 
of  a  small  known  amplitude  and  frequency  was  impressed  on  the  grid  of 
the  first  tube.  The  high-resistance  leak  r$  was  connected  across  C2  to 
insure  a  definite  value  of  the  grid  potential  during  the  experiment. 
The  effect  of  r0  upon  the  impedance  of  C2  was  negligible  because  C2  was 
large  (either  .05,  .1,  or  .2  MF)  and  the  frequencies  used  were  of  the 
order  of  io5. 

The  amplifier  was  a  two-tube  one  with  resistance  capacity  coupling. 
The  tubes  were  General  Electric  Company  tubes,  Radiatron  type  UV  201  ; 
they  were  used  with  the  filament  current  of  .94  ampere  and  had  a 
common  plate  voltage  supply  of  52.3  volts.  Separate  storage  cells 
supplied  each  filament.  The  plate  current  was  found  to  be  sensitive  to 
external  temperature  changes,  an  effect  explained,  perhaps,  by  the 
fluctuation  in  the  amount  of  the  absorbed  gases  in  the  glass  walls  of  the 
tubes.  It  was  therefore  found  necessary  to  enclose  the  electron  tubes  in 
covered  cardboard  tubes  in  order  to  keep  their  temperatures  constant. 
The  plate  battery  was  shunted  by  a  1.75  MF  condenser  C&.  The  re- 
sistance r2  was  115  X  io3  ohms  and  r3  was  360  X  io3  ohms.  The 
resistances  r0,  r2  and  rs  were  non-inductive,  being  of  the  type  described 
by  Hulburt.2  These  were  found  to  give  satisfactory  service.  The  value 
of  the  resistance  for  high-frequency  currents  was  assumed  the  same  as 
that  measured  with  direct  current. 

1  PHYS.  REV.,  16,  274,  1920. 

2  Loc.  cit. 


43 6  W.    C.    BROMBACHER. 

The  change  in  the  value  of  the  rectified  high-frequency  component  of 
the  plate  current  of  the  second  tube  of  the  amplifier,  designated  by  b0, 
was  measured  by  a  D'Arsonval  galvanometer,  G,  Fig.  I,  connected 
across  a  resistance  r4  placed  in  the  plate  circuit.  r4  was  60,000  ohms. 
The  galvanometer  had  a  resistance  of  9.0  ohms  and  a  sensibility  of 
5.8  X  io~8  amperes  per  millimeter  deflection  on  a  scale  125  cms.  distant. 
PI  and  P2,  Fig.  i,  were  potential  dividers,  PI  serving  to  keep  the  plate 
voltage  at  the  desired  value,  and  P2  to  compensate  for  the  potential  drop 
in  the  resistance  r4  so  that  the  galvanometer  rested  approximately  at 
zero.  When  the  grid  voltage  of  the  first  tube  was  changed,  a  deflection 
of  the  galvanometer  resulted  which  was  proportional  to  the  change  in  the 
rectified  high-frequency  component  of  the  output  plate  current. 

It  was  important  that  the  filament  currents  remain  constant.  Any 
change  in  these  currents  resulted  in  a  shift  of  the  operating  point  of  the 
tubes.  The  electron  tubes  were  seasoned  before  every  series  of  readings 
until  a  reasonably  constant  condition  of  filament  current  and  electron 
emission  was  reached.  In  order  to  eliminate  the  error  due  to  the  usual 
slow  drift  of  the  galvanometer,  the  two  zero  readings  were  averaged.  It 
was  found  that  the  grid  leak  r0  gave  a  constant  potential  of  nearly  zero 
on  the  grid  of  the  first  tube  when  its  value  was  246  X  io3  ohms.  This 
value  was  not  critical.  For  large  values  of  rQ,  the  value  of  the  grid 
potential  shifted  when  it  was  necessary  to  vary  the  value  of  C3.  A 
Kolster  decremeter,  calibrated  by  the  Bureau  of  Standards,  was  used 
to  determine  the  wave-lengths  of  the  high-frequency  current. 

3.   VARIATION  OF  COUPLING  CAPACITY. 

The  reading  of  the  coupling  condenser  C4  was  varied  at  each  reading, 
a  number  of  input  potentials  were  impressed  on  the  grid  of  the  first  tube 
and  the  corresponding  galvanometer  deflections  were  noted.  From  the 
reading  of  T,  the  thermo-galvanometer,  and  a  knowledge  of  the  capacities 
Ci,  Cz  and  €3,  the  amplitude  of  the  change  of  the  input  grid  voltage  A 
was  computed,  using  formula  (3).  Three  sets  of  readings  were  taken, 
at  wave-lengths  1016,  3070  and  6235  meters.  The  resulting  curves 
with  b0  the  ordinates  and  Az  the  abscissa,  are  shown  in  Figs.  2,  3  and  4. 
It  can  be  seen  that  for  each  value  of  C4  for  all  three  wave-lengths  the 
b0  —  Az  curves  are  straight  lines.  This  fact  has  been  established  by  a 
large  number  of  similar  curves,  not  shown  here.  The  curves  for  any  one 
wave-length  are  plotted  from  data  taken  with  the  potential  divider 
condensers  C2  and  C3  held  constant.  A  change  in  the  value  of  C*3  caused 
the  curve  for  any  particular  value  of  C4  to  shift  and  also  to  change  its 
slope.  This  is  shown  in  Fig.  3  by  the  curve  marked  628'.  This  fact 


VOL.  XX 

No. 


DETECTING  EFFICIENCY   OF   AMPLIFIER. 


437 


ZOO 


400  «  I0"! 


feOO 


Fig.  2. 


Fig.  3. 


can  be  explained  by  a  shift  in  the  operating  point  of  the  first  tube  because 
of  a  shift  in  the  normal  value  of  the  grid  potential.     r0  had  the  value 


20C 


50  100  150  . 10' 

Az  -  VOLTS2 

Fig.  4. 

13  X  io5  ohms  during  these  readings.     Another  point  of  interest  in  these 
curves  is  that  the  straight  lines  do  not  pass  through  the  origin,  although 


438 


W.   G.   BROMBACHER. 


[SECOND 
[SERIES. 


within  the  limit  of  experimental  error  they  pass  through  a  common 
point  on  the  A2  axis.  This  seems  to  indicate  a  constant  error  in  the 
determination  of  A2  although  a  check  up  of  the  calibrations  revealed  no 
differences  large  enough  for  compensation.  It  is  also  of  interest  to  notice 
that  for  each  wave-length  there  is  practically  the  same  current  range 
(&o)  but  that  there  is  a  large  range  in  the  value  of  A2-  for  1016  meters, 
.006  to  .015;  for  3070  meters,  .002  to  .005  and  for  6235  meters,  .0006  to 
.0015  volt2. 

The  main  fact,  however,  remains  that  the  straight  lines  were  obtained, 
as  is  predicted  by  formula  (i). 

In  order  to  further  test  formula  (i)  the  slopes  of  the  curves  corre- 
sponding to  each  value  of  £4  were  determined  and  then  plotted  against 
values  of  C4  for  each  of  the  three  wave-lengths  as  shown  in  Fig.  5.  That 


0 
40 

20 


•10' 


3070 


1016 


.C4    . 


200  400    MM  F     600 

Fig.  5. 

is,  experimental  values  of  b0/A2  are  plotted  against  values  of  C4.  Then, 
from  formula  (i)  the  theoretical  value  was  computed.  Values  of  the 
constants  not  before  given,  rit  the  direct-current  filament  to  plate  re- 
sistance of  the  first  tube,  was  60  X  io3  ohms;  C5,  the  filament-grid 
capacity  of  the  second  tube,  was  18  MMF.  This  was  measured  in  its 
socket  and  included  the  capacity  of  its  lead  wires,  which  were  short, 
however.  As  neither  n  or  k  were  determined  experimentally,  the  com- 
puted curve  was  made  to  coincide  with  the  experimental  curve  at  C4 


VOL.  XX. 
No.  5. 


DETECTING   EFFICIENCY   OF   AMPLIFIER. 


439 


equal  to  628  MMF.  The  computed  curves  are  the  broken  lines.  While 
the  agreement  between  the  experimental  and  computed  curve  is  not 
exact,  it  is  quite  satisfactory,  revealing  no  marked  differences  in  behavior 
for  two  of  the  wave-lengths  considered,  while  for  wave-length  3,070  m. 
the  agreement  is  good. 

No  change  in  the  character  of  the  computed  curve  was  found  whether 
formula  (2)  or  its  approximation  (i)  was  used. 

4.   VARIATION  OF  WAVE-LENGTH. 

The  coupling  capacity  C±  was  kept  at  its  maximum  value  of  628  MMF, 
ro,  r3  and  r4  remained  at  their  former  values  of  115  X  io3,  360  X  io3  and 
60  X  io3  ohms.  A  series  of  readings  were  taken  so  that  the  variation 
of  detecting  efficiency  with  wave-length  could  be  determined.  The 
experimental  results  are  given  in  the  full  line  curve  of  Fig.  6. 


80- 


40.10" 


0- 


o 


2000 


GOOO 


METERS         4000 
Fig.  6. 

As  the  curve  connecting  the  square  of  the  input  grid  potential  and 
the  rectified  component  of  output  plate  current  does  not  pass  through 
the  origin,  a  series  of  readings  was  taken  at  each  wave-length,  a  curve 
drawn  and  the  slope  determined.  This  slope  is  bo/A2.  The  experimental 
curves  just  mentioned  were  straight  lines  within  experimental  error. 

In  order  to  keep  the  grid  potential  of  the  first  tube  constant  for  the 
entire  range  of  wave-lengths  used,  it  was  found  necessary  to  fix  its  value 
near  zero,  which  was  done  by  making  TO  equal  246  X  io3  ohms.  This 
was  tested  by  obtaining  the  deflection  of  the  galvanometer  when  the 
condenser  C2  was  short  circuited,  there  being  no  high-frequency  current 
in  the  input  circuits.  This  test  was  made  when  the  condensers  C\  and 
Cs  had  values  corresponding  to  the  range  of  wave-lengths  used.  £2  was 
0.2  MMF  throughout  the  run. 

The  computed  curve,  shown  dotted  in  Fig.  6,  was  made  to  agree  with 
the  experimental  curve  in  the  neighborhood  of  2900  meters.  It  was 


44-O  W.   G.   BROMBACHRR. 

computed  from  formula  (2),  as  the  approximate  formula  (i)  differed 
with  it  over  the  range  of  wave-lengths  computed. 

The  agreement  of  the  two  curves  is  substantial  above  2,500  meters, 
and,  it  is  believed,  would  be  even  better,  if  the  apparatus  had  been 
used  with  better  control  over  the  grid  potentials.  The  poor  agreement 
at  lower  wave-lengths  is  due  to  the  difficulty  of  keeping  conditions 
constant  for  the  entire  range  of  observations.  An  unpublished  curve, 
detecting  efficiency  against  wave-length,  for  the  region  between  2,500- 
1,100  meters  gives  a  straight  line  of  about  the  same  slope  as  the  theoretical 
curve.  This  is  in  agreement  with  the  straight-line  relation  obtained  by 
Hulburt  between  600-1,600  meters.  Thus,  the  simple  theory  under- 
lying Hulburt's  formula  is  in  agreement  with  experiments  thus  far  made. 

It  is  seen  that  the  detecting  efficiency  at  higher  wave-lengths  (lower 
frequencies)  becomes  independent  of  the  wave-length. 

5.   AMPLIFICATION. 

It  was  necessary  to  test  the  independence  of  n  with  respect  to  wave- 
length. By  definition 


where  b0  is  the  rectified  component  of  the  output  plate  current  and  Eg 
is  the  amplitude  of  the  potential  variation  on  the  grid  of  the  second  tube. 

In  order  to  measure  n  the  input  voltage  was  impressed  directly  on  the 
second  tube,  the  first  tube  being  disconnected,  and  the  output  plate 
current  was  found  for  a  series  of  wave-lengths.  As  before,  sufficient 
observations  were  made  for  each  wave-length  so  that  a  curve  could  be 
drawn  and  the  slope  determined.  The  slope  was  bo/Eg2.  The  curves 
so  determined  were  straight  lines,  n  was  found  to  be  sensibly  constant 
for  all  wave-lengths  as  is  shown  in  Curve  3,  Fig.  6. 

If  the  ordinate  of  Curve  I  be  divided  by  the  ordihate  of  Curve  3  at 
the  same  wave-length,  both  of  Fig.  6,  the  quotient  is  the  amplification 
of  the  current  obtained  by  the  use  of  the  amplifying  electron  tube. 
That  is,  the  quotient  gives  the  number  of  times  the  rectified  component 
of  the  plate  current,  b0,  is  increased  by  the  use  of  two  tubes  instead  of 
one.  The  quotients,  or  current  amplifications,  are  the  ordinates  on  the 
right  margin  of  Fig.  6.  If  telephones  are  used  the  sound  intensity 
amplification  is  proportional  to  the  square  of  these  numbers. 

This  problem  was  suggested  to  me  by  Dr.  E.  O.  Hulburt,  now  at  the 
State  University  of  Iowa,  who  derived  the  formula  underlying  the 
investigation. 

JOHNS  HOPKINS  UNIVERSITY, 
June,  1922. 


BIOGRAPHICAL  NOTE. 

William  George  Brombacher,  son  of  Henry  and  Elizabeth  (Case) 
Brombacher,  was  born  in  Cleveland,  Ohio,  February  23,  1891.  He 
received  his  early  education  in  Chicago  High  Schools.  In  1915  he  re- 
ceived the  degree  of  Bachelor  of  Arts  from  Lake  Forest  College  with 
Shield  Honors  and  in  1917  the  degree  of  Master  of  Arts  from  the  same 
college.  The  year  1918  was  spent  in  the  United  States  Army,  stationed 
at  the  Bureau  of  Standards.  Upon  leaving  the  army  joined  the  Bureau 
of  Standards  staff. 

In  the  fall  of  1919  he  was  entered  at  the  Johns  Hopkins  University 
as  a  graduate  student  and  as  an  instructor  in  Physics.  He  followed  the 
courses  of  Professors  Ames,  Wood,  and  Pfund  in  Physics,  Professor 
Murnaghan  in  mathematics  and  Professor  Reid  in  Geophysics. 


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